Finite Difference and Finite Volume 1D Steady-State Heat Conduction Model for Machine Learning Algorithms

Machine learning is backbone of all the needs of the society. Mathematical models are backbone of machine learning algorithms. There are many mathematical models available for machine learning (ML). In thermodynamics field, there are many complex problems like fluid flow, heat transfer, etc. A good mathematical model is needed to solve such problem and to develop ML algorithms. To solve such kinds of problems, there are some mathematical methods have been developed to study the heat transfer problem. The aim of this paper is to optimize the best method to solve heat transfer problem for ML. In this paper, the Finite Difference Method (FDM) and Finite Volume Method (FVM) are evaluated by comparing the solutions for the 1D steady-state heat conduction problem with the heat generation source. Both methods were compared to the exact solution which has been performed and utilized as a baseline for the physical case in the current study. A problem of heat transfer in a rod is taken as an example to analyze and compare the computation performances of FVM and FDM. The results were obtained almost the same by both methods. However, the number of iterations in the FDM was fifty times more than FVM. It can be said that the FVM is more optimized than the FDM. All the methods, finite difference, finite volume, and exact solution have shown a good approach.